论文标题
跳跃的大波动率的功率式衍生物
Power-type derivatives for rough volatility with jumps
论文作者
论文摘要
在本文中，我们为波动性衍生物提出了一个新颖的定价围墙框架，同时考虑了大波动性和波动性的跳跃。我们的模型直接针对风险资产的瞬时差异，并由由Lévy下属驱动和独立的正弦波复合材料过程驱动的广义分数Ornstein-uhlenbeck过程组成。前一个成分捕获了瞬时波动性中的短期依赖性，而后者则是为了纠正平均正向方差的活性水平而引入的。这样的框架可确保以半闭合形式获得平均正向方差的特征功能，而无需调用任何几何均值近似值。为了分析掉期和欧洲风格的选项，平均向前波动率，我们在平均向前差异上引入了一类幂型衍生物，这也提供了灵活的非线性杠杆率。定价对冲公式基于修改的数值傅立叶变换技术。对VIX选项的两个独立的数据集进行了比较实证研究，在Covid-19大流行之前和期间进行了一项比较，以证明在各种内核选择下，提出的框架非常适合有效的模型校准。
In this paper we propose a novel pricing-hedging framework for volatility derivatives which simultaneously takes into account rough volatility and volatility jumps. Our model directly targets the instantaneous variance of a risky asset and consists of a generalized fractional Ornstein-Uhlenbeck process driven by a Lévy subordinator and an independent sinusoidal-composite Lévy process. The former component captures short-term dependence in the instantaneous volatility, while the latter is introduced expressly for rectifying the activity level of the average forward variance. Such a framework ensures that the characteristic function of average forward variance is obtainable in semi-closed form, without having to invoke any geometric-mean approximations. To analyze swaps and European-style options on average forward volatility, we introduce a general class of power-type derivatives on the average forward variance, which also provide flexible nonlinear leverage exposure. Pricing-hedging formulae are based on a modified numerical Fourier transform technique. A comparative empirical study is conducted on two independent recent data sets on VIX options, before and during the COVID-19 pandemic, to demonstrate that the proposed framework is highly amenable to efficient model calibration under various choices of kernels.
